Properties

Label 1900.2.a.k.1.1
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.56310016.1
Defining polynomial: \(x^{6} - 9 x^{4} + 14 x^{2} - 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.608430\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.28715 q^{3} +1.93210 q^{7} +7.80536 q^{9} +O(q^{10})\) \(q-3.28715 q^{3} +1.93210 q^{7} +7.80536 q^{9} +5.62981 q^{11} +2.07029 q^{13} -3.42535 q^{17} +1.00000 q^{19} -6.35109 q^{21} +5.35744 q^{23} -15.7959 q^{27} +1.09146 q^{29} +3.09146 q^{31} -18.5060 q^{33} -3.28715 q^{37} -6.80536 q^{39} -11.6107 q^{41} +0.501623 q^{43} +12.6470 q^{47} -3.26701 q^{49} +11.2596 q^{51} -3.01076 q^{53} -3.28715 q^{57} -2.35109 q^{59} +7.62981 q^{61} +15.0807 q^{63} -12.2324 q^{67} -17.6107 q^{69} +14.3511 q^{71} +2.87256 q^{73} +10.8773 q^{77} +4.00000 q^{79} +28.5075 q^{81} -5.35744 q^{83} -3.58780 q^{87} +8.35109 q^{89} +4.00000 q^{91} -10.1621 q^{93} -3.01076 q^{97} +43.9427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 10 q^{9} + O(q^{10}) \) \( 6 q + 10 q^{9} + 18 q^{11} + 6 q^{19} + 4 q^{21} - 4 q^{29} + 8 q^{31} - 4 q^{39} + 4 q^{41} + 12 q^{49} + 36 q^{51} + 28 q^{59} + 30 q^{61} - 32 q^{69} + 44 q^{71} + 24 q^{79} + 50 q^{81} + 8 q^{89} + 24 q^{91} + 90 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.28715 −1.89784 −0.948919 0.315521i \(-0.897821\pi\)
−0.948919 + 0.315521i \(0.897821\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.93210 0.730263 0.365132 0.930956i \(-0.381024\pi\)
0.365132 + 0.930956i \(0.381024\pi\)
\(8\) 0 0
\(9\) 7.80536 2.60179
\(10\) 0 0
\(11\) 5.62981 1.69745 0.848726 0.528832i \(-0.177370\pi\)
0.848726 + 0.528832i \(0.177370\pi\)
\(12\) 0 0
\(13\) 2.07029 0.574195 0.287098 0.957901i \(-0.407310\pi\)
0.287098 + 0.957901i \(0.407310\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.42535 −0.830768 −0.415384 0.909646i \(-0.636353\pi\)
−0.415384 + 0.909646i \(0.636353\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −6.35109 −1.38592
\(22\) 0 0
\(23\) 5.35744 1.11710 0.558552 0.829470i \(-0.311357\pi\)
0.558552 + 0.829470i \(0.311357\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −15.7959 −3.03993
\(28\) 0 0
\(29\) 1.09146 0.202679 0.101340 0.994852i \(-0.467687\pi\)
0.101340 + 0.994852i \(0.467687\pi\)
\(30\) 0 0
\(31\) 3.09146 0.555243 0.277622 0.960691i \(-0.410454\pi\)
0.277622 + 0.960691i \(0.410454\pi\)
\(32\) 0 0
\(33\) −18.5060 −3.22149
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.28715 −0.540404 −0.270202 0.962804i \(-0.587091\pi\)
−0.270202 + 0.962804i \(0.587091\pi\)
\(38\) 0 0
\(39\) −6.80536 −1.08973
\(40\) 0 0
\(41\) −11.6107 −1.81329 −0.906645 0.421895i \(-0.861365\pi\)
−0.906645 + 0.421895i \(0.861365\pi\)
\(42\) 0 0
\(43\) 0.501623 0.0764968 0.0382484 0.999268i \(-0.487822\pi\)
0.0382484 + 0.999268i \(0.487822\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.6470 1.84475 0.922376 0.386294i \(-0.126245\pi\)
0.922376 + 0.386294i \(0.126245\pi\)
\(48\) 0 0
\(49\) −3.26701 −0.466715
\(50\) 0 0
\(51\) 11.2596 1.57666
\(52\) 0 0
\(53\) −3.01076 −0.413560 −0.206780 0.978388i \(-0.566298\pi\)
−0.206780 + 0.978388i \(0.566298\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.28715 −0.435394
\(58\) 0 0
\(59\) −2.35109 −0.306086 −0.153043 0.988220i \(-0.548907\pi\)
−0.153043 + 0.988220i \(0.548907\pi\)
\(60\) 0 0
\(61\) 7.62981 0.976897 0.488449 0.872593i \(-0.337563\pi\)
0.488449 + 0.872593i \(0.337563\pi\)
\(62\) 0 0
\(63\) 15.0807 1.89999
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.2324 −1.49442 −0.747212 0.664585i \(-0.768608\pi\)
−0.747212 + 0.664585i \(0.768608\pi\)
\(68\) 0 0
\(69\) −17.6107 −2.12008
\(70\) 0 0
\(71\) 14.3511 1.70316 0.851580 0.524224i \(-0.175645\pi\)
0.851580 + 0.524224i \(0.175645\pi\)
\(72\) 0 0
\(73\) 2.87256 0.336208 0.168104 0.985769i \(-0.446236\pi\)
0.168104 + 0.985769i \(0.446236\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.8773 1.23959
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 28.5075 3.16750
\(82\) 0 0
\(83\) −5.35744 −0.588056 −0.294028 0.955797i \(-0.594996\pi\)
−0.294028 + 0.955797i \(0.594996\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.58780 −0.384653
\(88\) 0 0
\(89\) 8.35109 0.885214 0.442607 0.896716i \(-0.354054\pi\)
0.442607 + 0.896716i \(0.354054\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) −10.1621 −1.05376
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.01076 −0.305696 −0.152848 0.988250i \(-0.548845\pi\)
−0.152848 + 0.988250i \(0.548845\pi\)
\(98\) 0 0
\(99\) 43.9427 4.41641
\(100\) 0 0
\(101\) −4.80536 −0.478151 −0.239075 0.971001i \(-0.576844\pi\)
−0.239075 + 0.971001i \(0.576844\pi\)
\(102\) 0 0
\(103\) 4.22762 0.416560 0.208280 0.978069i \(-0.433214\pi\)
0.208280 + 0.978069i \(0.433214\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.92098 0.862424 0.431212 0.902251i \(-0.358086\pi\)
0.431212 + 0.902251i \(0.358086\pi\)
\(108\) 0 0
\(109\) 5.25963 0.503781 0.251890 0.967756i \(-0.418948\pi\)
0.251890 + 0.967756i \(0.418948\pi\)
\(110\) 0 0
\(111\) 10.8054 1.02560
\(112\) 0 0
\(113\) 12.5088 1.17673 0.588364 0.808596i \(-0.299772\pi\)
0.588364 + 0.808596i \(0.299772\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16.1594 1.49393
\(118\) 0 0
\(119\) −6.61810 −0.606680
\(120\) 0 0
\(121\) 20.6948 1.88135
\(122\) 0 0
\(123\) 38.1662 3.44133
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.2952 1.09102 0.545510 0.838104i \(-0.316336\pi\)
0.545510 + 0.838104i \(0.316336\pi\)
\(128\) 0 0
\(129\) −1.64891 −0.145179
\(130\) 0 0
\(131\) −10.7863 −0.942400 −0.471200 0.882026i \(-0.656179\pi\)
−0.471200 + 0.882026i \(0.656179\pi\)
\(132\) 0 0
\(133\) 1.93210 0.167534
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.85582 −0.414861 −0.207430 0.978250i \(-0.566510\pi\)
−0.207430 + 0.978250i \(0.566510\pi\)
\(138\) 0 0
\(139\) −11.2405 −0.953409 −0.476705 0.879064i \(-0.658169\pi\)
−0.476705 + 0.879064i \(0.658169\pi\)
\(140\) 0 0
\(141\) −41.5725 −3.50104
\(142\) 0 0
\(143\) 11.6554 0.974669
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 10.7391 0.885750
\(148\) 0 0
\(149\) 3.62981 0.297366 0.148683 0.988885i \(-0.452497\pi\)
0.148683 + 0.988885i \(0.452497\pi\)
\(150\) 0 0
\(151\) −10.3511 −0.842360 −0.421180 0.906977i \(-0.638384\pi\)
−0.421180 + 0.906977i \(0.638384\pi\)
\(152\) 0 0
\(153\) −26.7360 −2.16148
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 7.12708 0.568803 0.284402 0.958705i \(-0.408205\pi\)
0.284402 + 0.958705i \(0.408205\pi\)
\(158\) 0 0
\(159\) 9.89682 0.784869
\(160\) 0 0
\(161\) 10.3511 0.815780
\(162\) 0 0
\(163\) 1.21686 0.0953118 0.0476559 0.998864i \(-0.484825\pi\)
0.0476559 + 0.998864i \(0.484825\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.8830 1.22906 0.614531 0.788893i \(-0.289345\pi\)
0.614531 + 0.788893i \(0.289345\pi\)
\(168\) 0 0
\(169\) −8.71390 −0.670300
\(170\) 0 0
\(171\) 7.80536 0.596891
\(172\) 0 0
\(173\) −13.7884 −1.04831 −0.524157 0.851622i \(-0.675620\pi\)
−0.524157 + 0.851622i \(0.675620\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.72838 0.580901
\(178\) 0 0
\(179\) 10.3511 0.773677 0.386838 0.922148i \(-0.373567\pi\)
0.386838 + 0.922148i \(0.373567\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −25.0803 −1.85399
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −19.2841 −1.41019
\(188\) 0 0
\(189\) −30.5193 −2.21995
\(190\) 0 0
\(191\) −8.43517 −0.610348 −0.305174 0.952297i \(-0.598715\pi\)
−0.305174 + 0.952297i \(0.598715\pi\)
\(192\) 0 0
\(193\) 23.2864 1.67619 0.838097 0.545521i \(-0.183668\pi\)
0.838097 + 0.545521i \(0.183668\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.28116 −0.590008 −0.295004 0.955496i \(-0.595321\pi\)
−0.295004 + 0.955496i \(0.595321\pi\)
\(198\) 0 0
\(199\) −18.7863 −1.33172 −0.665861 0.746076i \(-0.731936\pi\)
−0.665861 + 0.746076i \(0.731936\pi\)
\(200\) 0 0
\(201\) 40.2097 2.83617
\(202\) 0 0
\(203\) 2.10881 0.148009
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 41.8167 2.90646
\(208\) 0 0
\(209\) 5.62981 0.389422
\(210\) 0 0
\(211\) −21.7789 −1.49932 −0.749660 0.661823i \(-0.769783\pi\)
−0.749660 + 0.661823i \(0.769783\pi\)
\(212\) 0 0
\(213\) −47.1742 −3.23232
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 5.97300 0.405474
\(218\) 0 0
\(219\) −9.44255 −0.638068
\(220\) 0 0
\(221\) −7.09146 −0.477023
\(222\) 0 0
\(223\) 14.5548 0.974662 0.487331 0.873217i \(-0.337970\pi\)
0.487331 + 0.873217i \(0.337970\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.07029 0.137410 0.0687050 0.997637i \(-0.478113\pi\)
0.0687050 + 0.997637i \(0.478113\pi\)
\(228\) 0 0
\(229\) −15.4616 −1.02173 −0.510867 0.859660i \(-0.670676\pi\)
−0.510867 + 0.859660i \(0.670676\pi\)
\(230\) 0 0
\(231\) −35.7554 −2.35254
\(232\) 0 0
\(233\) 28.8934 1.89287 0.946434 0.322897i \(-0.104657\pi\)
0.946434 + 0.322897i \(0.104657\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −13.1486 −0.854093
\(238\) 0 0
\(239\) 26.6181 1.72178 0.860891 0.508790i \(-0.169907\pi\)
0.860891 + 0.508790i \(0.169907\pi\)
\(240\) 0 0
\(241\) −19.6107 −1.26324 −0.631619 0.775279i \(-0.717609\pi\)
−0.631619 + 0.775279i \(0.717609\pi\)
\(242\) 0 0
\(243\) −46.3208 −2.97148
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.07029 0.131729
\(248\) 0 0
\(249\) 17.6107 1.11603
\(250\) 0 0
\(251\) 14.2522 0.899594 0.449797 0.893131i \(-0.351496\pi\)
0.449797 + 0.893131i \(0.351496\pi\)
\(252\) 0 0
\(253\) 30.1614 1.89623
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.2919 0.704371 0.352185 0.935930i \(-0.385439\pi\)
0.352185 + 0.935930i \(0.385439\pi\)
\(258\) 0 0
\(259\) −6.35109 −0.394637
\(260\) 0 0
\(261\) 8.51925 0.527329
\(262\) 0 0
\(263\) −15.3571 −0.946959 −0.473479 0.880805i \(-0.657002\pi\)
−0.473479 + 0.880805i \(0.657002\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −27.4513 −1.67999
\(268\) 0 0
\(269\) 11.4426 0.697665 0.348832 0.937185i \(-0.386578\pi\)
0.348832 + 0.937185i \(0.386578\pi\)
\(270\) 0 0
\(271\) 12.4161 0.754223 0.377111 0.926168i \(-0.376917\pi\)
0.377111 + 0.926168i \(0.376917\pi\)
\(272\) 0 0
\(273\) −13.1486 −0.795790
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −16.0212 −0.962619 −0.481309 0.876551i \(-0.659839\pi\)
−0.481309 + 0.876551i \(0.659839\pi\)
\(278\) 0 0
\(279\) 24.1300 1.44462
\(280\) 0 0
\(281\) −24.8851 −1.48452 −0.742260 0.670112i \(-0.766246\pi\)
−0.742260 + 0.670112i \(0.766246\pi\)
\(282\) 0 0
\(283\) 16.2348 0.965057 0.482529 0.875880i \(-0.339718\pi\)
0.482529 + 0.875880i \(0.339718\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.4330 −1.32418
\(288\) 0 0
\(289\) −5.26701 −0.309824
\(290\) 0 0
\(291\) 9.89682 0.580162
\(292\) 0 0
\(293\) 23.2864 1.36041 0.680204 0.733023i \(-0.261891\pi\)
0.680204 + 0.733023i \(0.261891\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −88.9282 −5.16013
\(298\) 0 0
\(299\) 11.0915 0.641436
\(300\) 0 0
\(301\) 0.969184 0.0558628
\(302\) 0 0
\(303\) 15.7959 0.907453
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.964728 0.0550599 0.0275300 0.999621i \(-0.491236\pi\)
0.0275300 + 0.999621i \(0.491236\pi\)
\(308\) 0 0
\(309\) −13.8968 −0.790562
\(310\) 0 0
\(311\) 18.1638 1.02998 0.514988 0.857197i \(-0.327796\pi\)
0.514988 + 0.857197i \(0.327796\pi\)
\(312\) 0 0
\(313\) 7.30116 0.412686 0.206343 0.978480i \(-0.433844\pi\)
0.206343 + 0.978480i \(0.433844\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.64135 −0.429181 −0.214590 0.976704i \(-0.568842\pi\)
−0.214590 + 0.976704i \(0.568842\pi\)
\(318\) 0 0
\(319\) 6.14473 0.344039
\(320\) 0 0
\(321\) −29.3246 −1.63674
\(322\) 0 0
\(323\) −3.42535 −0.190591
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −17.2892 −0.956094
\(328\) 0 0
\(329\) 24.4352 1.34715
\(330\) 0 0
\(331\) 22.3129 1.22643 0.613214 0.789917i \(-0.289876\pi\)
0.613214 + 0.789917i \(0.289876\pi\)
\(332\) 0 0
\(333\) −25.6574 −1.40602
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.790654 0.0430696 0.0215348 0.999768i \(-0.493145\pi\)
0.0215348 + 0.999768i \(0.493145\pi\)
\(338\) 0 0
\(339\) −41.1183 −2.23324
\(340\) 0 0
\(341\) 17.4044 0.942499
\(342\) 0 0
\(343\) −19.8368 −1.07109
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.95361 −0.426972 −0.213486 0.976946i \(-0.568482\pi\)
−0.213486 + 0.976946i \(0.568482\pi\)
\(348\) 0 0
\(349\) 15.8777 0.849915 0.424957 0.905213i \(-0.360289\pi\)
0.424957 + 0.905213i \(0.360289\pi\)
\(350\) 0 0
\(351\) −32.7022 −1.74551
\(352\) 0 0
\(353\) 8.45524 0.450027 0.225013 0.974356i \(-0.427757\pi\)
0.225013 + 0.974356i \(0.427757\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 21.7547 1.15138
\(358\) 0 0
\(359\) 15.2787 0.806380 0.403190 0.915116i \(-0.367901\pi\)
0.403190 + 0.915116i \(0.367901\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −68.0269 −3.57049
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 25.6331 1.33804 0.669019 0.743245i \(-0.266714\pi\)
0.669019 + 0.743245i \(0.266714\pi\)
\(368\) 0 0
\(369\) −90.6258 −4.71779
\(370\) 0 0
\(371\) −5.81708 −0.302008
\(372\) 0 0
\(373\) 1.30390 0.0675132 0.0337566 0.999430i \(-0.489253\pi\)
0.0337566 + 0.999430i \(0.489253\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.25964 0.116378
\(378\) 0 0
\(379\) 4.87034 0.250173 0.125086 0.992146i \(-0.460079\pi\)
0.125086 + 0.992146i \(0.460079\pi\)
\(380\) 0 0
\(381\) −40.4161 −2.07058
\(382\) 0 0
\(383\) −20.6876 −1.05709 −0.528544 0.848906i \(-0.677262\pi\)
−0.528544 + 0.848906i \(0.677262\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.91535 0.199028
\(388\) 0 0
\(389\) 0.252246 0.0127894 0.00639470 0.999980i \(-0.497964\pi\)
0.00639470 + 0.999980i \(0.497964\pi\)
\(390\) 0 0
\(391\) −18.3511 −0.928054
\(392\) 0 0
\(393\) 35.4561 1.78852
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −28.1665 −1.41364 −0.706819 0.707395i \(-0.749870\pi\)
−0.706819 + 0.707395i \(0.749870\pi\)
\(398\) 0 0
\(399\) −6.35109 −0.317952
\(400\) 0 0
\(401\) 5.25963 0.262653 0.131327 0.991339i \(-0.458076\pi\)
0.131327 + 0.991339i \(0.458076\pi\)
\(402\) 0 0
\(403\) 6.40023 0.318818
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −18.5060 −0.917310
\(408\) 0 0
\(409\) −25.0533 −1.23880 −0.619402 0.785074i \(-0.712625\pi\)
−0.619402 + 0.785074i \(0.712625\pi\)
\(410\) 0 0
\(411\) 15.9618 0.787338
\(412\) 0 0
\(413\) −4.54253 −0.223523
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 36.9493 1.80942
\(418\) 0 0
\(419\) 12.7022 0.620542 0.310271 0.950648i \(-0.399580\pi\)
0.310271 + 0.950648i \(0.399580\pi\)
\(420\) 0 0
\(421\) 13.9618 0.680457 0.340228 0.940343i \(-0.389496\pi\)
0.340228 + 0.940343i \(0.389496\pi\)
\(422\) 0 0
\(423\) 98.7142 4.79965
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 14.7415 0.713393
\(428\) 0 0
\(429\) −38.3129 −1.84976
\(430\) 0 0
\(431\) 36.1300 1.74032 0.870160 0.492770i \(-0.164016\pi\)
0.870160 + 0.492770i \(0.164016\pi\)
\(432\) 0 0
\(433\) −5.50726 −0.264662 −0.132331 0.991206i \(-0.542246\pi\)
−0.132331 + 0.991206i \(0.542246\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.35744 0.256281
\(438\) 0 0
\(439\) −34.4811 −1.64569 −0.822846 0.568265i \(-0.807615\pi\)
−0.822846 + 0.568265i \(0.807615\pi\)
\(440\) 0 0
\(441\) −25.5002 −1.21429
\(442\) 0 0
\(443\) 28.9562 1.37575 0.687874 0.725830i \(-0.258544\pi\)
0.687874 + 0.725830i \(0.258544\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −11.9317 −0.564352
\(448\) 0 0
\(449\) −15.5725 −0.734913 −0.367456 0.930041i \(-0.619771\pi\)
−0.367456 + 0.930041i \(0.619771\pi\)
\(450\) 0 0
\(451\) −65.3662 −3.07797
\(452\) 0 0
\(453\) 34.0256 1.59866
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.715236 −0.0334573 −0.0167287 0.999860i \(-0.505325\pi\)
−0.0167287 + 0.999860i \(0.505325\pi\)
\(458\) 0 0
\(459\) 54.1065 2.52548
\(460\) 0 0
\(461\) −28.7863 −1.34071 −0.670355 0.742041i \(-0.733858\pi\)
−0.670355 + 0.742041i \(0.733858\pi\)
\(462\) 0 0
\(463\) −22.1055 −1.02733 −0.513664 0.857991i \(-0.671712\pi\)
−0.513664 + 0.857991i \(0.671712\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −37.6645 −1.74291 −0.871454 0.490478i \(-0.836822\pi\)
−0.871454 + 0.490478i \(0.836822\pi\)
\(468\) 0 0
\(469\) −23.6342 −1.09132
\(470\) 0 0
\(471\) −23.4278 −1.07950
\(472\) 0 0
\(473\) 2.82405 0.129850
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −23.5001 −1.07599
\(478\) 0 0
\(479\) −5.32461 −0.243288 −0.121644 0.992574i \(-0.538817\pi\)
−0.121644 + 0.992574i \(0.538817\pi\)
\(480\) 0 0
\(481\) −6.80536 −0.310298
\(482\) 0 0
\(483\) −34.0256 −1.54822
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.9425 0.677109 0.338555 0.940947i \(-0.390062\pi\)
0.338555 + 0.940947i \(0.390062\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 5.81708 0.262521 0.131260 0.991348i \(-0.458098\pi\)
0.131260 + 0.991348i \(0.458098\pi\)
\(492\) 0 0
\(493\) −3.73864 −0.168380
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 27.7277 1.24376
\(498\) 0 0
\(499\) 17.4235 0.779981 0.389990 0.920819i \(-0.372478\pi\)
0.389990 + 0.920819i \(0.372478\pi\)
\(500\) 0 0
\(501\) −52.2097 −2.33256
\(502\) 0 0
\(503\) −0.490004 −0.0218482 −0.0109241 0.999940i \(-0.503477\pi\)
−0.0109241 + 0.999940i \(0.503477\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 28.6439 1.27212
\(508\) 0 0
\(509\) 16.4811 0.730510 0.365255 0.930908i \(-0.380982\pi\)
0.365255 + 0.930908i \(0.380982\pi\)
\(510\) 0 0
\(511\) 5.55007 0.245521
\(512\) 0 0
\(513\) −15.7959 −0.697407
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 71.2001 3.13138
\(518\) 0 0
\(519\) 45.3246 1.98953
\(520\) 0 0
\(521\) 17.0533 0.747117 0.373559 0.927607i \(-0.378137\pi\)
0.373559 + 0.927607i \(0.378137\pi\)
\(522\) 0 0
\(523\) −34.2777 −1.49886 −0.749430 0.662084i \(-0.769672\pi\)
−0.749430 + 0.662084i \(0.769672\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.5893 −0.461278
\(528\) 0 0
\(529\) 5.70218 0.247921
\(530\) 0 0
\(531\) −18.3511 −0.796369
\(532\) 0 0
\(533\) −24.0376 −1.04118
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −34.0256 −1.46831
\(538\) 0 0
\(539\) −18.3926 −0.792227
\(540\) 0 0
\(541\) 29.9427 1.28734 0.643669 0.765304i \(-0.277411\pi\)
0.643669 + 0.765304i \(0.277411\pi\)
\(542\) 0 0
\(543\) 6.57430 0.282130
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −29.1339 −1.24568 −0.622838 0.782351i \(-0.714020\pi\)
−0.622838 + 0.782351i \(0.714020\pi\)
\(548\) 0 0
\(549\) 59.5534 2.54168
\(550\) 0 0
\(551\) 1.09146 0.0464979
\(552\) 0 0
\(553\) 7.72838 0.328644
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 38.4542 1.62936 0.814678 0.579914i \(-0.196914\pi\)
0.814678 + 0.579914i \(0.196914\pi\)
\(558\) 0 0
\(559\) 1.03851 0.0439241
\(560\) 0 0
\(561\) 63.3896 2.67631
\(562\) 0 0
\(563\) 8.58181 0.361680 0.180840 0.983512i \(-0.442118\pi\)
0.180840 + 0.983512i \(0.442118\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 55.0793 2.31311
\(568\) 0 0
\(569\) −0.221120 −0.00926985 −0.00463492 0.999989i \(-0.501475\pi\)
−0.00463492 + 0.999989i \(0.501475\pi\)
\(570\) 0 0
\(571\) 2.23315 0.0934544 0.0467272 0.998908i \(-0.485121\pi\)
0.0467272 + 0.998908i \(0.485121\pi\)
\(572\) 0 0
\(573\) 27.7277 1.15834
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16.6225 0.692002 0.346001 0.938234i \(-0.387539\pi\)
0.346001 + 0.938234i \(0.387539\pi\)
\(578\) 0 0
\(579\) −76.5460 −3.18114
\(580\) 0 0
\(581\) −10.3511 −0.429436
\(582\) 0 0
\(583\) −16.9500 −0.701998
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.2213 −0.793347 −0.396674 0.917960i \(-0.629835\pi\)
−0.396674 + 0.917960i \(0.629835\pi\)
\(588\) 0 0
\(589\) 3.09146 0.127381
\(590\) 0 0
\(591\) 27.2214 1.11974
\(592\) 0 0
\(593\) −13.0230 −0.534792 −0.267396 0.963587i \(-0.586163\pi\)
−0.267396 + 0.963587i \(0.586163\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 61.7533 2.52739
\(598\) 0 0
\(599\) 27.0915 1.10693 0.553464 0.832873i \(-0.313306\pi\)
0.553464 + 0.832873i \(0.313306\pi\)
\(600\) 0 0
\(601\) −5.42779 −0.221404 −0.110702 0.993854i \(-0.535310\pi\)
−0.110702 + 0.993854i \(0.535310\pi\)
\(602\) 0 0
\(603\) −95.4782 −3.88817
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −21.0663 −0.855056 −0.427528 0.904002i \(-0.640616\pi\)
−0.427528 + 0.904002i \(0.640616\pi\)
\(608\) 0 0
\(609\) −6.93197 −0.280898
\(610\) 0 0
\(611\) 26.1829 1.05925
\(612\) 0 0
\(613\) 30.2753 1.22281 0.611405 0.791318i \(-0.290605\pi\)
0.611405 + 0.791318i \(0.290605\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.3049 1.82391 0.911953 0.410295i \(-0.134574\pi\)
0.911953 + 0.410295i \(0.134574\pi\)
\(618\) 0 0
\(619\) 18.2331 0.732852 0.366426 0.930447i \(-0.380581\pi\)
0.366426 + 0.930447i \(0.380581\pi\)
\(620\) 0 0
\(621\) −84.6258 −3.39592
\(622\) 0 0
\(623\) 16.1351 0.646439
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −18.5060 −0.739060
\(628\) 0 0
\(629\) 11.2596 0.448951
\(630\) 0 0
\(631\) −11.4087 −0.454173 −0.227086 0.973875i \(-0.572920\pi\)
−0.227086 + 0.973875i \(0.572920\pi\)
\(632\) 0 0
\(633\) 71.5905 2.84547
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.76365 −0.267986
\(638\) 0 0
\(639\) 112.015 4.43126
\(640\) 0 0
\(641\) 4.92330 0.194459 0.0972293 0.995262i \(-0.469002\pi\)
0.0972293 + 0.995262i \(0.469002\pi\)
\(642\) 0 0
\(643\) −24.4136 −0.962779 −0.481390 0.876507i \(-0.659868\pi\)
−0.481390 + 0.876507i \(0.659868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11.0424 0.434123 0.217061 0.976158i \(-0.430353\pi\)
0.217061 + 0.976158i \(0.430353\pi\)
\(648\) 0 0
\(649\) −13.2362 −0.519566
\(650\) 0 0
\(651\) −19.6342 −0.769523
\(652\) 0 0
\(653\) −28.1665 −1.10224 −0.551121 0.834426i \(-0.685800\pi\)
−0.551121 + 0.834426i \(0.685800\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 22.4214 0.874742
\(658\) 0 0
\(659\) 4.74037 0.184659 0.0923294 0.995729i \(-0.470569\pi\)
0.0923294 + 0.995729i \(0.470569\pi\)
\(660\) 0 0
\(661\) −19.4426 −0.756228 −0.378114 0.925759i \(-0.623427\pi\)
−0.378114 + 0.925759i \(0.623427\pi\)
\(662\) 0 0
\(663\) 23.3107 0.905313
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.84744 0.226414
\(668\) 0 0
\(669\) −47.8439 −1.84975
\(670\) 0 0
\(671\) 42.9544 1.65824
\(672\) 0 0
\(673\) −12.5088 −0.482178 −0.241089 0.970503i \(-0.577505\pi\)
−0.241089 + 0.970503i \(0.577505\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 40.7265 1.56525 0.782623 0.622497i \(-0.213882\pi\)
0.782623 + 0.622497i \(0.213882\pi\)
\(678\) 0 0
\(679\) −5.81708 −0.223239
\(680\) 0 0
\(681\) −6.80536 −0.260782
\(682\) 0 0
\(683\) −14.8312 −0.567500 −0.283750 0.958898i \(-0.591579\pi\)
−0.283750 + 0.958898i \(0.591579\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 50.8248 1.93909
\(688\) 0 0
\(689\) −6.23315 −0.237464
\(690\) 0 0
\(691\) 13.0958 0.498188 0.249094 0.968479i \(-0.419867\pi\)
0.249094 + 0.968479i \(0.419867\pi\)
\(692\) 0 0
\(693\) 84.9015 3.22514
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 39.7707 1.50642
\(698\) 0 0
\(699\) −94.9769 −3.59236
\(700\) 0 0
\(701\) −14.0797 −0.531785 −0.265892 0.964003i \(-0.585667\pi\)
−0.265892 + 0.964003i \(0.585667\pi\)
\(702\) 0 0
\(703\) −3.28715 −0.123977
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.28441 −0.349176
\(708\) 0 0
\(709\) 8.38928 0.315066 0.157533 0.987514i \(-0.449646\pi\)
0.157533 + 0.987514i \(0.449646\pi\)
\(710\) 0 0
\(711\) 31.2214 1.17090
\(712\) 0 0
\(713\) 16.5623 0.620264
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −87.4977 −3.26766
\(718\) 0 0
\(719\) 6.70652 0.250111 0.125055 0.992150i \(-0.460089\pi\)
0.125055 + 0.992150i \(0.460089\pi\)
\(720\) 0 0
\(721\) 8.16816 0.304198
\(722\) 0 0
\(723\) 64.4634 2.39742
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 20.5009 0.760337 0.380168 0.924917i \(-0.375866\pi\)
0.380168 + 0.924917i \(0.375866\pi\)
\(728\) 0 0
\(729\) 66.7407 2.47188
\(730\) 0 0
\(731\) −1.71823 −0.0635512
\(732\) 0 0
\(733\) −42.4323 −1.56727 −0.783636 0.621220i \(-0.786637\pi\)
−0.783636 + 0.621220i \(0.786637\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −68.8661 −2.53671
\(738\) 0 0
\(739\) 44.4352 1.63457 0.817287 0.576231i \(-0.195477\pi\)
0.817287 + 0.576231i \(0.195477\pi\)
\(740\) 0 0
\(741\) −6.80536 −0.250001
\(742\) 0 0
\(743\) −36.4350 −1.33667 −0.668336 0.743859i \(-0.732993\pi\)
−0.668336 + 0.743859i \(0.732993\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −41.8167 −1.52999
\(748\) 0 0
\(749\) 17.2362 0.629797
\(750\) 0 0
\(751\) −29.6107 −1.08051 −0.540255 0.841501i \(-0.681672\pi\)
−0.540255 + 0.841501i \(0.681672\pi\)
\(752\) 0 0
\(753\) −46.8493 −1.70728
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −44.0252 −1.60012 −0.800062 0.599917i \(-0.795200\pi\)
−0.800062 + 0.599917i \(0.795200\pi\)
\(758\) 0 0
\(759\) −99.1450 −3.59874
\(760\) 0 0
\(761\) 25.9809 0.941807 0.470903 0.882185i \(-0.343928\pi\)
0.470903 + 0.882185i \(0.343928\pi\)
\(762\) 0 0
\(763\) 10.1621 0.367893
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.86744 −0.175753
\(768\) 0 0
\(769\) 2.68308 0.0967543 0.0483772 0.998829i \(-0.484595\pi\)
0.0483772 + 0.998829i \(0.484595\pi\)
\(770\) 0 0
\(771\) −37.1183 −1.33678
\(772\) 0 0
\(773\) 39.5328 1.42190 0.710949 0.703244i \(-0.248266\pi\)
0.710949 + 0.703244i \(0.248266\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 20.8770 0.748958
\(778\) 0 0
\(779\) −11.6107 −0.415997
\(780\) 0 0
\(781\) 80.7940 2.89103
\(782\) 0 0
\(783\) −17.2407 −0.616131
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −9.15783 −0.326442 −0.163221 0.986590i \(-0.552188\pi\)
−0.163221 + 0.986590i \(0.552188\pi\)
\(788\) 0 0
\(789\) 50.4811 1.79717
\(790\) 0 0
\(791\) 24.1682 0.859321
\(792\) 0 0
\(793\) 15.7959 0.560930
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.5581 0.551095 0.275547 0.961287i \(-0.411141\pi\)
0.275547 + 0.961287i \(0.411141\pi\)
\(798\) 0 0
\(799\) −43.3203 −1.53256
\(800\) 0 0
\(801\) 65.1832 2.30314
\(802\) 0 0
\(803\) 16.1720 0.570698
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −37.6134 −1.32405
\(808\) 0 0
\(809\) −41.6184 −1.46323 −0.731613 0.681721i \(-0.761232\pi\)
−0.731613 + 0.681721i \(0.761232\pi\)
\(810\) 0 0
\(811\) −49.1685 −1.72654 −0.863269 0.504744i \(-0.831587\pi\)
−0.863269 + 0.504744i \(0.831587\pi\)
\(812\) 0 0
\(813\) −40.8135 −1.43139
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.501623 0.0175496
\(818\) 0 0
\(819\) 31.2214 1.09097
\(820\) 0 0
\(821\) −13.9012 −0.485154 −0.242577 0.970132i \(-0.577993\pi\)
−0.242577 + 0.970132i \(0.577993\pi\)
\(822\) 0 0
\(823\) 19.0704 0.664754 0.332377 0.943147i \(-0.392149\pi\)
0.332377 + 0.943147i \(0.392149\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −46.7712 −1.62639 −0.813197 0.581988i \(-0.802275\pi\)
−0.813197 + 0.581988i \(0.802275\pi\)
\(828\) 0 0
\(829\) 2.37452 0.0824706 0.0412353 0.999149i \(-0.486871\pi\)
0.0412353 + 0.999149i \(0.486871\pi\)
\(830\) 0 0
\(831\) 52.6640 1.82689
\(832\) 0 0
\(833\) 11.1906 0.387732
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −48.8325 −1.68790
\(838\) 0 0
\(839\) −1.57252 −0.0542894 −0.0271447 0.999632i \(-0.508641\pi\)
−0.0271447 + 0.999632i \(0.508641\pi\)
\(840\) 0 0
\(841\) −27.8087 −0.958921
\(842\) 0 0
\(843\) 81.8011 2.81738
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 39.9843 1.37388
\(848\) 0 0
\(849\) −53.3662 −1.83152
\(850\) 0 0
\(851\) −17.6107 −0.603688
\(852\) 0 0
\(853\) 1.88094 0.0644021 0.0322010 0.999481i \(-0.489748\pi\)
0.0322010 + 0.999481i \(0.489748\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 17.0371 0.581975 0.290987 0.956727i \(-0.406016\pi\)
0.290987 + 0.956727i \(0.406016\pi\)
\(858\) 0 0
\(859\) 49.8395 1.70050 0.850251 0.526377i \(-0.176450\pi\)
0.850251 + 0.526377i \(0.176450\pi\)
\(860\) 0 0
\(861\) 73.7407 2.51308
\(862\) 0 0
\(863\) 12.1696 0.414258 0.207129 0.978314i \(-0.433588\pi\)
0.207129 + 0.978314i \(0.433588\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 17.3134 0.587995
\(868\) 0 0
\(869\) 22.5193 0.763913
\(870\) 0 0
\(871\) −25.3246 −0.858092
\(872\) 0 0
\(873\) −23.5001 −0.795356
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −42.2287 −1.42596 −0.712981 0.701184i \(-0.752655\pi\)
−0.712981 + 0.701184i \(0.752655\pi\)
\(878\) 0 0
\(879\) −76.5460 −2.58183
\(880\) 0 0
\(881\) −12.6683 −0.426807 −0.213403 0.976964i \(-0.568455\pi\)
−0.213403 + 0.976964i \(0.568455\pi\)
\(882\) 0 0
\(883\) −11.5414 −0.388400 −0.194200 0.980962i \(-0.562211\pi\)
−0.194200 + 0.980962i \(0.562211\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6.36171 0.213605 0.106803 0.994280i \(-0.465939\pi\)
0.106803 + 0.994280i \(0.465939\pi\)
\(888\) 0 0
\(889\) 23.7554 0.796732
\(890\) 0 0
\(891\) 160.492 5.37669
\(892\) 0 0
\(893\) 12.6470 0.423215
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −36.4593 −1.21734
\(898\) 0 0
\(899\) 3.37421 0.112536
\(900\) 0 0
\(901\) 10.3129 0.343572
\(902\) 0 0
\(903\) −3.18585 −0.106019
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 24.9538 0.828576 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(908\) 0 0
\(909\) −37.5075 −1.24405
\(910\) 0 0
\(911\) −28.6640 −0.949680 −0.474840 0.880072i \(-0.657494\pi\)
−0.474840 + 0.880072i \(0.657494\pi\)
\(912\) 0 0
\(913\) −30.1614 −0.998196
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20.8401 −0.688200
\(918\) 0 0
\(919\) −25.0385 −0.825944 −0.412972 0.910744i \(-0.635509\pi\)
−0.412972 + 0.910744i \(0.635509\pi\)
\(920\) 0 0
\(921\) −3.17121 −0.104495
\(922\) 0 0
\(923\) 29.7109 0.977947
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 32.9981 1.08380
\(928\) 0 0
\(929\) 27.2744 0.894844 0.447422 0.894323i \(-0.352342\pi\)
0.447422 + 0.894323i \(0.352342\pi\)
\(930\) 0 0
\(931\) −3.26701 −0.107072
\(932\) 0 0
\(933\) −59.7072 −1.95473
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28.7193 −0.938219 −0.469109 0.883140i \(-0.655425\pi\)
−0.469109 + 0.883140i \(0.655425\pi\)
\(938\) 0 0
\(939\) −24.0000 −0.783210
\(940\) 0 0
\(941\) 7.81708 0.254829 0.127415 0.991850i \(-0.459332\pi\)
0.127415 + 0.991850i \(0.459332\pi\)
\(942\) 0 0
\(943\) −62.2037 −2.02563
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −40.4886 −1.31570 −0.657851 0.753148i \(-0.728534\pi\)
−0.657851 + 0.753148i \(0.728534\pi\)
\(948\) 0 0
\(949\) 5.94704 0.193049
\(950\) 0 0
\(951\) 25.1183 0.814515
\(952\) 0 0
\(953\) −7.57857 −0.245494 −0.122747 0.992438i \(-0.539170\pi\)
−0.122747 + 0.992438i \(0.539170\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −20.1986 −0.652930
\(958\) 0 0
\(959\) −9.38190 −0.302958
\(960\) 0 0
\(961\) −21.4429 −0.691705
\(962\) 0 0
\(963\) 69.6315 2.24384
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −15.5195 −0.499075 −0.249537 0.968365i \(-0.580279\pi\)
−0.249537 + 0.968365i \(0.580279\pi\)
\(968\) 0 0
\(969\) 11.2596 0.361711
\(970\) 0 0
\(971\) 1.81708 0.0583127 0.0291564 0.999575i \(-0.490718\pi\)
0.0291564 + 0.999575i \(0.490718\pi\)
\(972\) 0 0
\(973\) −21.7178 −0.696240
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −21.0178 −0.672420 −0.336210 0.941787i \(-0.609145\pi\)
−0.336210 + 0.941787i \(0.609145\pi\)
\(978\) 0 0
\(979\) 47.0151 1.50261
\(980\) 0 0
\(981\) 41.0533 1.31073
\(982\) 0 0
\(983\) −19.2339 −0.613467 −0.306733 0.951795i \(-0.599236\pi\)
−0.306733 + 0.951795i \(0.599236\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −80.3221 −2.55668
\(988\) 0 0
\(989\) 2.68742 0.0854549
\(990\) 0 0
\(991\) 36.1682 1.14892 0.574460 0.818533i \(-0.305212\pi\)
0.574460 + 0.818533i \(0.305212\pi\)
\(992\) 0 0
\(993\) −73.3458 −2.32756
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 35.6955 1.13049 0.565245 0.824923i \(-0.308782\pi\)
0.565245 + 0.824923i \(0.308782\pi\)
\(998\) 0 0
\(999\) 51.9236 1.64279
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1900.2.a.k.1.1 6
4.3 odd 2 7600.2.a.cj.1.6 6
5.2 odd 4 380.2.c.b.229.6 yes 6
5.3 odd 4 380.2.c.b.229.1 6
5.4 even 2 inner 1900.2.a.k.1.6 6
15.2 even 4 3420.2.f.c.1369.1 6
15.8 even 4 3420.2.f.c.1369.2 6
20.3 even 4 1520.2.d.i.609.6 6
20.7 even 4 1520.2.d.i.609.1 6
20.19 odd 2 7600.2.a.cj.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.c.b.229.1 6 5.3 odd 4
380.2.c.b.229.6 yes 6 5.2 odd 4
1520.2.d.i.609.1 6 20.7 even 4
1520.2.d.i.609.6 6 20.3 even 4
1900.2.a.k.1.1 6 1.1 even 1 trivial
1900.2.a.k.1.6 6 5.4 even 2 inner
3420.2.f.c.1369.1 6 15.2 even 4
3420.2.f.c.1369.2 6 15.8 even 4
7600.2.a.cj.1.1 6 20.19 odd 2
7600.2.a.cj.1.6 6 4.3 odd 2